In the case of dealing with a color pictorial image as data, respective pixels forming that pictorial image are ordinarily represented by the combination of density values of three primary colors. In practice, for three primary colors used, various ones are used depending upon media for dealing with color pictorial image. For example, generally, for displaying a pictorial image on a CRT, etc., three primary colors of the R (Red), G (Green) and B (Blue) system are used, and in the case of printing three primary colors of the C (Cyan), M (Magenta) and Y (Yellow) system are used. In addition, even in the case of three primary colors of the same CMY system, they would become different colors, respectively, in dependence upon the hue peculiar to an ink used in a printing machine or a printer.
As just described above, for permitting the same pictorial image to be dealt with different media, it is required to make a color modification so as to become in conformity with the representation by the three primary colors peculiar to a media used. For such a color modification method, two approaches have been mainly put into practice up to now. The first approach is a method to define a color cube having coordinate axes of the three dimensional rectangular coordinate system on which density values of the three primary colors are taken, respectively, to store modified or corrected data into a storage unit corresponding to the color cube. Data which has not yet modified is used as an address value to provide an access to one point within the color cube defined in the storage unit to read out modified data memorized with respect to this point to thereby make a color modification. This method is disclosed, e.g., in the Japanese Patent Publication No. 16403/77. However, when modified data are stored in respect of all the points within the color cube as stated above, an extensive memory capacity is required. For this reason, a high cost and large capacity memory unit must be prepared. To overcome this drawback, a method for reducing a necessary memory capacity to realize a reduced cost is disclosed in the Japanese Patent Publication No. 25416/80. In accordance with this method, modified data are stored only in respect of representative points within the color cube. Further, when intermediate values between adjacent representative points are needed, an interpolation operation is carried out. Moreover, in a method disclosed in the Japanese Patent publication No. 30222/80, for permitting the memory capacity to be further reduced, only data corresponding to differences between modified data and predetermined reference values are memorized instead of memorizing modified data themselves in regard to respective representative points.
The second approach for the color modification method is a method to use a masking equation. For example, for transforming a pictorial image of the RGB system to a pictorial image of the CMY system, a linear masking equation expressed by EQU C=a.sub.11 R+a.sub.12 G+a.sub.13 B EQU M=a.sub.21 R+a.sub.22 G+a.sub.23 B EQU Y=a.sub.31 R+a.sub.32 G+a.sub.33 B
is used where R, G, B, C, M and Y are variables indicative of density values of primary colors, respectively, and a.sub.11 to a.sub.33 are called "linear or first degree masking coefficients", which are parameters to govern transformation, respectively. In this example, these nine parameters are set so that the pictorial image represented by the RGB system and the pictorial image represented by the CMY system are equivalent to each other. Ordinarily, nine parameters are determined by the ratio of the maximum densities of the three primary colors.
Color modification using the linear masking equation has been described as an example. In addition, a method using a quadratic equation to further reduce modification error is also known. In this method, quadratic or second degree terms of R.sup.2, G.sup.2 and B.sup.2 and RG, GB and BR are introduced in the equation in addition to the linear terms of R, G and B. Ordinarily, by selecting several pixels as respective sampling pixels to perform an operation using the method of least squares so that an error between the representation of the RGB system and the representation of the CMY system is minimized, these nine parameters are set. It is to be noted that such a conventional color modification method is described in detail, e.g., in "Theory of Color Reproduction" by J. A. C. Yule (edited by the publication division of the Printing Society, 1971), and therefore, this material should be referred to in connection with the detail.
However, there are drawbacks encountered with these conventional color modification methods, respectively. In the case of the method by the first approach, i.e., the method of storing modified data into a storage unit corresponding to the color cube, when modified data are stored in respect to all the points within the color cube, an extensive memory capacity is required. For example, in the case of representing one color with a tone of 256 stages, it is required for color modification of the three primary colors to store data as large as those of 256.sup.3 sets into the storage unit. In addition, because core memory or semiconductor memory must be used for making a high speed access, cost of the memory unit becomes extremely high. To avoid this, when modified data are stored only in respect to representative points within the color cube, the interpolation operation is required, resulting in another problem that the high speed processing becomes difficult.
Also with the method by the second approach, i.e., the method using the masking equation, there is a problem as described below. First, since the color modification method using the linear masking equation is on the premises of the proportional rule indicating that the density ratio of the three primary colors of an ink should be maintained at the same value if the absolute value thereof is equally multiplied, and the additive rule indicating that the three primary color densities when superposition print is conducted should be equal to sum of densities of individual inks, sufficient color modification cannot be made. Especially, since the proportional rule and the additive rule are not both fully satisfied in actual media of the CMY system based on the substrative color mixture, even if color modification based on the linear masking equation is conducted, sufficient color reproducibility cannot be provided between the pictorial image in the medium before transformation and the pictorial image in the medium after transformation.
On the other hand, the conventional color modification method using the quadratic masking equation has a more improved color reproducibility as compared to the method using the linear masking equation, but has the problem that the equation becomes complicated, resulting in an elongated computational time.